The paper presents the analysis of vibrations of the crankshaft system and proposition of its modelling. At the beginning there are general information about the torsional vibration dampers. Moreover, models of different kinds of dampers are shown with their governing equations. The next section presents proposition of the algorithm of modelling of the crank-piston mechanism with a torsional vibrations damper. Furthermore, there are equations of motion of the analyzed system in this chapter. After that, the results of numerical simulations and experiments are shown. Finally, the paper is summarized by giving conclusions about the analysis of crankshaft systems with a dynamic eliminator of vibrations and their modelling.